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Derivada de la función/ arctg/ x^(-x)/ tg(7x)/ x^(-x)^3*arctg(7x)^4

Derivada de x^(-x)^3*arctg(7x)^4

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
 /    3\           
 \(-x) /     4     
x       *atan (7*x)
x(−x)3atan⁡4(7x)x^{\left(- x\right)^{3}} \operatorname{atan}^{4}{\left(7 x \right)} 
x^((-x)^3)*atan(7*x)^4
Primera derivada [src] 
                                               /    3\           
 /    3\            /  3               \       \(-x) /     3     
 \(-x) /     4      |-x        2       |   28*x       *atan (7*x)
x       *atan (7*x)*|---- - 3*x *log(x)| + ----------------------
                    \ x                /                 2       
                                                 1 + 49*x
x(−x)3(−3x2log⁡(x)+(−1)x3x)atan⁡4(7x)+28x(−x)3atan⁡3(7x)49x2+1x^{\left(- x\right)^{3}} \left(- 3 x^{2} \log{\left(x \right)} + \frac{\left(-1\right) x^{3}}{x}\right) \operatorname{atan}^{4}{\left(7 x \right)} + \frac{28 x^{\left(- x\right)^{3}} \operatorname{atan}^{3}{\left(7 x \right)}}{49 x^{2} + 1}
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Segunda derivada [src] 
    3            /                                                                                   2                         \
  -x      2      |196*(-3 + 14*x*atan(7*x))         2      /                3               2\   56*x *(1 + 3*log(x))*atan(7*x)|
-x   *atan (7*x)*|------------------------- + x*atan (7*x)*\5 + 6*log(x) - x *(1 + 3*log(x)) / + ------------------------------|
                 |                  2                                                                              2           |
                 |       /        2\                                                                       1 + 49*x            |
                 \       \1 + 49*x /                                                                                           /
−x−x3(56x2(3log⁡(x)+1)atan⁡(7x)49x2+1+x(−x3(3log⁡(x)+1)2+6log⁡(x)+5)atan⁡2(7x)+196(14xatan⁡(7x)−3)(49x2+1)2)atan⁡2(7x)- x^{- x^{3}} \left(\frac{56 x^{2} \left(3 \log{\left(x \right)} + 1\right) \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} + x \left(- x^{3} \left(3 \log{\left(x \right)} + 1\right)^{2} + 6 \log{\left(x \right)} + 5\right) \operatorname{atan}^{2}{\left(7 x \right)} + \frac{196 \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right)}{\left(49 x^{2} + 1\right)^{2}}\right) \operatorname{atan}^{2}{\left(7 x \right)}
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Tercera derivada [src] 
     /                                                                                              /                                                 2     2     \                                                                                                              \          
     |                                                                                              |      2            3       63*x*atan(7*x)   196*x *atan (7*x)|                                                                                                              |          
     |                                                                                         2744*|- atan (7*x) + --------- - -------------- + -----------------|                                                                                                              |          
   3 |                                                                                              |                       2             2                  2    |            2      /                3               2\        2                                               |          
 -x  |      3      /                 6               3      3                              \        \               1 + 49*x      1 + 49*x           1 + 49*x     /   84*x*atan (7*x)*\5 + 6*log(x) - x *(1 + 3*log(x)) /   588*x *(1 + 3*log(x))*(-3 + 14*x*atan(7*x))*atan(7*x)|          
x   *|- atan (7*x)*\11 + 6*log(x) + x *(1 + 3*log(x))  - 3*x *(1 + 3*log(x))*(5 + 6*log(x))/ + -------------------------------------------------------------------- - --------------------------------------------------- + -----------------------------------------------------|*atan(7*x)
     |                                                                                                                                2                                                            2                                                        2                    |          
     |                                                                                                                     /        2\                                                     1 + 49*x                                              /        2\                     |          
     \                                                                                                                     \1 + 49*x /                                                                                                           \1 + 49*x /                     /
x−x3(588x2(14xatan⁡(7x)−3)(3log⁡(x)+1)atan⁡(7x)(49x2+1)2−84x(−x3(3log⁡(x)+1)2+6log⁡(x)+5)atan⁡2(7x)49x2+1−(x6(3log⁡(x)+1)3−3x3(3log⁡(x)+1)(6log⁡(x)+5)+6log⁡(x)+11)atan⁡3(7x)+2744(196x2atan⁡2(7x)49x2+1−63xatan⁡(7x)49x2+1−atan⁡2(7x)+349x2+1)(49x2+1)2)atan⁡(7x)x^{- x^{3}} \left(\frac{588 x^{2} \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right) \left(3 \log{\left(x \right)} + 1\right) \operatorname{atan}{\left(7 x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{84 x \left(- x^{3} \left(3 \log{\left(x \right)} + 1\right)^{2} + 6 \log{\left(x \right)} + 5\right) \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \left(x^{6} \left(3 \log{\left(x \right)} + 1\right)^{3} - 3 x^{3} \left(3 \log{\left(x \right)} + 1\right) \left(6 \log{\left(x \right)} + 5\right) + 6 \log{\left(x \right)} + 11\right) \operatorname{atan}^{3}{\left(7 x \right)} + \frac{2744 \left(\frac{196 x^{2} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{63 x \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{atan}^{2}{\left(7 x \right)} + \frac{3}{49 x^{2} + 1}\right)}{\left(49 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(7 x \right)}
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